System and method for generating a low discrepancy curve on an abstract surface

• US 20020135578A1
• Filed: 06/08/2001
• Published: 09/26/2002
• Est. Priority Date: 02/05/2001
• Status: Active Grant

• Current Assignee: National Instruments Corporation (Emerson Electric Company)
• Original Assignee: National Instruments Corporation (Emerson Electric Company)
• Inventors: Nair, Dinesh, Wenzel, Lothar, Rajagopal, Ram
• Granted Patent: US 6,909,801 B2
• Time in Patent Office: Days
• US Class Current: 345/442
• CPC Class Codes: G05B 19/41815 characterised by the cooperation between machine tools, manipulators and conveyor or other workpiece supply system, workcell
• CPC Class Codes: G05B 2219/32212 If parameter out of tolerance reject product
• CPC Class Codes: G05B 2219/40554 Object recognition to track object on conveyor
• CPC Class Codes: G06F 17/10 Complex mathematical operations function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544
• CPC Class Codes: G06Q 10/047 Optimisation of routes or paths, e.g. travelling salesman problem
• CPC Class Codes: G06T 7/0004 Industrial image inspection
• CPC Class Codes: G06V 10/10 Image acquisition document image scanning and transmission H04N1/00; control of digital cameras H04N23/60
• CPC Class Codes: G06V 10/42 Global feature extraction by analysis of the whole pattern, e.g. using frequency domain transformations or autocorrelation
• CPC Class Codes: G06V 10/421 by analysing segments intersecting the pattern
• CPC Class Codes: Y02P 90/02 Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

A system and method for generating a curve, such as a Low Discrepancy Curve, on a surface, such as an abstract surface with a Riemannian metric. The system may comprise a computer which includes a CPU and a memory medium which is operable to store one or more programs executable by the CPU to perform the method. The method may: 1) parameterize the surface; 2) select a curve, such as a Low Discrepancy Curve, in a parameter space, for example, a simple space such as a unit square; 3) re-parameterize the surface, for example, re-parameterize the surface such that a ratio of line and area elements of the surface based on a Riemannian metric is constant; and 4) map the curve onto the surface using the re-parameterization. The method may also generate output comprising information regarding the mapped curve, for example, displaying the mapped curve on a display device.

Claims

1. A method for generating a curve on a surface, comprising:

selecting a parameterization of the surface, wherein the parameterization corresponds to a parameter space;

selecting a first curve in the parameter space;

determining a re-parameterization of the surface based on a metric of the surface; and

mapping the first curve in the parameter space onto the surface based on the re-parameterization, to generate the curve;

wherein the curve is useable in analyzing the surface.

2. The method of claim 1, further comprising:

generating output comprising the generated curve on the surface.

3. The method of claim 1,

wherein the first curve is a Low Discrepancy Curve in the parameter space;

and

wherein the generated curve is a Low Discrepancy Curve on the surface.

4. The method of claim 1, wherein the parameter space comprises a 2D rectangle.

5. The method of claim 1, wherein the parameter space comprises one of a unit square, a unit cube, or a unit hyper-cube.

6. The method of claim 1, wherein the parameter space comprises a unit n-dimensional cube, wherein the dimensionality n is greater than 4.

7. The method of claim 1, wherein the metric of the surface is a Riemannian metric.

8. The method of claim 1, wherein the surface comprises a space with dimensionality greater than two.

9. The method of claim 1,

wherein the surface comprises a six-dimensional space comprising three position degrees of freedom and three orientation degrees of freedom for an object;

and

wherein the generated curve comprises a scan path useable in scanning the space.

10. The method of claim 9, further comprising:

scanning the space, wherein said scanning the space is performed to determine an optimum position and orientation for the object.

15. The method of claim 1,

wherein the first curve is a Low Discrepancy Curve in the parameter space;

and

wherein the generated curve is a Low Discrepancy Curve on the surface.

16. The method of claim 1, wherein the parameter space comprises a 2D rectangle.

17. The method of claim 1, wherein the parameter space comprises one of a unit square, a unit cube, or a unit hyper-cube.

18. The method of claim 1, wherein the parameter space comprises a unit n-dimensional cube, wherein the dimensionality n is greater than 4.

19. The method of claim 1, wherein the metric of the surface is a Riemannian metric.

20. The method of claim 1, wherein the surface comprises a space with dimensionality greater than two.

11. A method for generating a curve on a surface of an object, comprising:

selecting a parameterization of the surface, wherein the parameterization corresponds to a parameter space;

selecting a first curve in the parameter space;

determining a re-parameterization of the surface based on a metric of the surface; and

mapping the first curve in the parameter space onto the surface based on the re-parameterization, to generate the curve;

wherein the curve is useable in analyzing the object.

12. The method of claim 11, further comprising:

generating output comprising the generated curve on the surface.

13. The method of claim 11, further comprising:

analyzing the object using the curve.

14. The method of claim 11, further comprising:

determining a property of the object using the curve.

21. A memory medium which is operable to store program instructions for generating a curve on a surface, wherein said program instructions are executable to perform:

storing a parameterization of the surface, wherein the parameterization corresponds to a parameter space;

storing a first curve in the parameter space;

determining a re-parameterization of the surface based on a metric of the surface; and

mapping the first curve in the parameter space onto the surface based on the re-parameterization, to generate the curve;

wherein the curve is useable in analyzing the surface.

22. The memory medium of claim 21, wherein the program instructions are further executable to perform:

generating output comprising the generated curve on the surface.

23. The memory medium of claim 21,

wherein the first curve is a Low Discrepancy Curve in the parameter space;

and

wherein the generated curve is a Low Discrepancy Curve on the surface.

24. The memory medium of claim 21, wherein the parameter space comprises one of a 2D rectangle, a unit square, a unit cube, or a unit hyper-cube.

25. The memory medium of claim 21, wherein the parameter space comprises a unit n-dimensional cube, wherein the dimensionality n is greater than 4.

26. The memory medium of claim 21, wherein the metric of the surface is a Riemannian metric.

27. The memory medium of claim 21, wherein the surface comprises a space with dimensionality greater than two.

28. The memory medium of claim 21,

wherein the surface comprises a surface of an object;

wherein the curve comprises a scan path useable to scan the object;

wherein the program instructions are further executable to perform;

scanning the object to determine one or more properties of the object.

29. The memory medium of claim 21,

wherein the surface comprises a six-dimensional space comprising three position degrees of freedom and three orientation degrees of freedom for an object;

wherein the generated curve comprises a scan path useable in scanning the six-dimensional space;

wherein the program instructions are further executable to perform;

scanning the six-dimensional space to determine an optimum position and orientation of the object.

30. A system for generating a curve on a surface, comprising:

aCPU; and

a memory medium which is operable to store one or more software programs;

wherein said CPU is operable to execute said one or more software programs to perform;

selecting a parameterization of the surface, wherein the parameterization corresponds to a parameter space;

selecting a first curve in the parameter space;

determining a re-parameterization of the surface based on a metric of the surface; and

mapping the first curve in the parameter space onto the surface based on the re-parameterization, to generate the curve;

wherein the curve is useable in analyzing the surface.

31. The system of claim 30, wherein the CPU is further operable to execute said one or more software programs to perform:

generating output comprising the generated curve on the surface.

32. The system of claim 30,

wherein the first curve is a Low Discrepancy Curve in the parameter space;

and

wherein the generated curve is a Low Discrepancy Curve on the surface.

33. The system of claim 30, wherein the parameter space comprises one of a 2D rectangle, a unit square, a unit cube, a unit hyper-cube, or a unit n-dimensional cube,

wherein the dimensionality n is greater than 4.

34. The system of claim 30, wherein the metric of the surface is a Riemannian metric.

35. The system of claim 30, wherein the surface comprises a space with dimensionality greater than two.